Analyzing many-body localization with a quantum computer

Abstract

Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical simulations have so far been limited to a small number of sites, making it difficult to obtain reliable statements about the thermodynamic limit. In this paper, we explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed. The limitations of quantum measurement, which preclude the possibility of directly obtaining the entanglement entropy, make it difficult to apply some of the definitions of many-body localization used in the recent literature. We discuss alternative tests of localization that can be implemented on a quantum computer.

11 pages, 8 figures; slightly revised, published version

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• Early breakdown of area-law entanglement at many-body delocalization transition
• Efficient variational diagonalization of fully many-body localized Hamiltonians
• Particle-hole symmetry, many-body localization, and topological edge modes
• Dynamical many-body localization in an integrable model
• Lower Bounds for the Trotter Error
• Simulation of open quantum systems on universal quantum computers
• Inducing a transition between thermal and many-body localized states and detecting many-body mobility edges through dissipation